Answer:
The perimeter is 14 units
Step-by-step explanation:
Given
[tex]A = (-2,2)[/tex]
[tex]B = (1,2)[/tex]
[tex]C = (1,-2)[/tex]
[tex]D = (-2,-2)[/tex]
Required
Determine the perimeter
To do this, we simply calculate the distance between the sides of the rectangle i.e. AB, BC, CD and DA.
Distance (d) is calculated using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
For AB
[tex]A = (-2,2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B = (1,2)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]AB = \sqrt{(-2 - 1)^2 + (2 - 2)^2} = \sqrt{9} = 3[/tex]
For BC
[tex]B = (1,2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]C = (1,-2)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]BC = \sqrt{(1-1)^2 + (2--2)^2} = \sqrt{16} = 4[/tex]
For CD
[tex]C = (1,-2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]D = (-2,-2)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]CD = \sqrt{(1 - -2)^2 + (-2 -- 2)^2} = \sqrt{9} = 3[/tex]
For DA
[tex]D = (-2,-2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]A = (-2,2)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]DA = \sqrt{(-2--2)^2 + (-2-2)^2} = \sqrt{16} = 4[/tex]
So, the perimeter (P) is:
[tex]P = AB + BC + CD + DA[/tex]
[tex]P = 3 +4 + 3 + 4[/tex]
[tex]P = 14[/tex]
The perimeter is 14 units
